Baseline carried forward missing data assumptions

Question

Researchers assessed the effectiveness of a range of weight management programmes for weight loss. A randomised controlled trial study design, incorporating eight treatment arms, was used. Each intervention-Weight Watchers, Slimming World, Rosemary Conley, group-based dietetics led programme, general practice one to one counselling, pharmacy led one to one counselling, and a choice of any of the six programmes-lasted for 12 weeks. The control treatment consisted of 12 vouchers enabling free entrance to a local leisure (fitness) centre. Participants were 740 obese or overweight men and women identified from general practice records. The primary outcome was weight loss at the end of the programme (12 weeks). Secondary outcomes included weight loss at one year. Baseline characteristics were available for all participants, whereas follow-up data were available for 658 (88.9%) participants at the end of the programme and 522 (70.5%) at one year. Analyses were performed according to intention to treat, using “baseline observation carried forward” to account for missing data. All treatment programmes achieved significant weight loss from baseline to programme end. When compared with the control treatment at 12 weeks, the only programmes that resulted in significantly more weight loss were Weight Watchers (mean difference 2.53 kg, 95% confidence interval 1.30 to 3.76; P<0.001) and Rosemary Conley (2.18, 0.96 to 3.41; P=0.004). All programmes except general practice and pharmacy provision resulted in significant weight loss at one year. At one year, only the Weight Watchers programme resulted in significantly greater weight loss than the control treatment (2.5 kg, 0.8 to 4.2; P=0.022). It was concluded that commercially provided weight management services are more effective than primary care-based services.

If missing data were imputed using baseline carried forward (BCF) method, then what is the assumption that the researchers made about the weight distribution of the participants who did not have their weight measured at 12 weeks and one year. Based on your judgement about the assumption do you think the BCF is a suitable method of imputation?

Under the BCF assumption do you think the trial provided biased/unbiased answers?

If the researchers had not imputed missing data, but just used complete cases, which assumption of the randomisation would be violated?

Comment on what happens to power if the researchers would have just used complete cases?

When one analyses the data using intention to treat do you think that the researchers are answering the question that they are interested in?

Intention to treat defined here as patients are analysed according to the treatment they were randomised to receive. Baseline carried forward method defined here as using the baseline observation in place of the end-point observation. Akin to last observation carried forward that uses the last observation in place of the end treatment. Here baseline measures of patients weight used at end point of 12 weeks As far as my understanding goes, I believe that by using BCF reserachers are assuming the weight distribtion will remain the same across the trial, and this will provide bias conclusions. If complete cases had been used, then balance / exchangability between groups would be violated I am unsure of the relationsip with power following reduced cases, my inital thinking is that the power will be reduced with a smaller sample size, but would like clarification on the relationship power, and missing data analysis. My understanding of ITT analyses is that it will answer the intended research question, ignoring cross over effects as such. Using a conservative approach to answer the question of interest. I am not 100% sure of my reasoning about this however.

Any clarification on these points would be greatly appreciated

Answer 1

Power of Welch One-Way ANOVA with Missing Data.

This is a simulation to address the power issue. In a somewhat simpler design than yours I have a one-factor ANOVA with three levels of the factor and five replications for each factor. Sample means are unequal $\mu_1 = 50, \mu_2 = 52, \mu_3 = 55$ with $\sigma = 2.$ I use the Welch oneway test in R which does not assume equal variances. (If variances happen to be equal, as here, then results are nearly the same as for the pooled t test.)

Full design. This design has power approximately 0.83 of correctly rejecting the null hypothesis that all three group means are equal.

set.seed(1234)
g = as.factor(rep(1:3, each=5))
mu = rep(c(50,52,55), each=5)
sg = 2
pv = replicate(10^4, oneway.test(rnorm(15,mu,sg)~g)$p.val)
mean(pv <= .05)
[1] 0.8256

One missing observation. However, if one of the replications in Group 3 is missing, the power drops to about 0.75.

g = as.factor(rep(1:3, times=c(5,5,4)))
mu = rep(c(50,52,55), times=(c(5,5,4)))
sg = 2
pvm = replicate(10^4, oneway.test(rnorm(14,mu,sg)~g)$p.val)
mean(pvm <= .05)
[1] 0.7471

Note: Many statistical software packages have power and sample size procedures, so that one can plan the number of replications in each group in order to have a sufficiently high power to make the experiment worthwhile. However, these procedures do not generally compute power for designs that are unbalanced due to missing data.